Certainly! Let's solve this step-by-step:
We are given two expressions:
- [tex]\( JM = 5x - 8 \)[/tex]
- [tex]\( LM = 2x - 6 \)[/tex]
We need to determine an expression for [tex]\( JL \)[/tex], which is the sum of [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex].
1. Write the expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]:
[tex]\[
JM = 5x - 8
\][/tex]
[tex]\[
LM = 2x - 6
\][/tex]
2. Add the expressions to find [tex]\( JL \)[/tex]:
[tex]\[
JL = JM + LM
\][/tex]
Substitute the given expressions for [tex]\( JM \)[/tex] and [tex]\( LM \)[/tex]:
[tex]\[
JL = (5x - 8) + (2x - 6)
\][/tex]
3. Combine like terms:
[tex]\[
JL = 5x + 2x - 8 - 6
\][/tex]
Simplify the expression:
[tex]\[
JL = 7x - 14
\][/tex]
So, the expression that represents [tex]\( JL \)[/tex] is [tex]\( 7x - 14 \)[/tex].
Among the given options, the correct one is:
[tex]\[ \boxed{7x - 14} \][/tex]
